LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit A100 47.97s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit A100 47.97s (1) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "acbb1161-1dfb-41e5-df1a-932595de3142"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701141191.1377995\n",
            "Tue Nov 28 03:13:11 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "# !pip install pennylane custatevec-cu11 pennylane-lightning-kokkos\n",
        "\n",
        "import time\n",
        "seconds = time.time()\n",
        "print(\"Time in seconds since beginning of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "aa42a975-629a-4ee8-e854-3b148712ef77"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.07 0.75 0.37]\n",
            " [0.75 0.99 0.77]\n",
            " [0.37 0.77 0.5 ]]\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def create_data_point(n):\n",
        "    \"\"\"\n",
        "    Returns a random undirected adjacency matrix of dimension (n,n).\n",
        "    The diagonal elements are interpreted as node attributes.\n",
        "    \"\"\"\n",
        "    mat = np.random.rand(n, n)\n",
        "    A = (mat + np.transpose(mat))/2\n",
        "    return np.round(A, decimals=2)\n",
        "\n",
        "A = create_data_point(3)\n",
        "print(A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fZNWu6j_jAmh"
      },
      "source": [
        "Let\\'s also write a function to generate permuted versions of this\n",
        "adjacency matrix.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "7e71bb94-3808-48ac-c6c0-9c12e46c6923"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.99 0.77 0.75]\n",
            " [0.77 0.5  0.37]\n",
            " [0.75 0.37 0.07]]\n"
          ]
        }
      ],
      "source": [
        "def permute(A, permutation):\n",
        "    \"\"\"\n",
        "    Returns a copy of A with rows and columns swapped according to permutation.\n",
        "    For example, the permutation [1, 2, 0] swaps 0->1, 1->2, 2->0.\n",
        "    \"\"\"\n",
        "\n",
        "    P = np.zeros((len(A), len(A)))\n",
        "    for i,j in enumerate(permutation):\n",
        "        P[i,j] = 1\n",
        "\n",
        "    return P @ A @ np.transpose(P)\n",
        "\n",
        "A_perm = permute(A, [1, 2, 0])\n",
        "print(A_perm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Js9CqRTZjAmi"
      },
      "source": [
        "If we create [networkx]{.title-ref} graphs from both adjacency matrices\n",
        "and plot them, we see that they are identical as claimed.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "a1060d2f-b307-44b4-8b42-e5ede6d1c0e3"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
        "\n",
        "# interpret diagonal of matrix as node attributes\n",
        "node_labels = {n: A[n,n] for n in range(len(A))}\n",
        "np.fill_diagonal(A, np.zeros(len(A)))\n",
        "\n",
        "G1 = nx.Graph(A)\n",
        "pos1=nx.spring_layout(G1)\n",
        "nx.draw(G1, pos1, labels=node_labels, ax=ax1, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G1,'weight')\n",
        "nx.draw_networkx_edge_labels(G1,pos1,edge_labels=edge_labels, ax=ax1)\n",
        "\n",
        "# interpret diagonal of permuted matrix as node attributes\n",
        "node_labels = {n: A_perm[n,n] for n in range(len(A_perm))}\n",
        "np.fill_diagonal(A_perm, np.zeros(len(A)))\n",
        "\n",
        "G2 = nx.Graph(A_perm)\n",
        "pos2=nx.spring_layout(G2)\n",
        "nx.draw(G2, pos2, labels=node_labels, ax=ax2, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G2,'weight')\n",
        "nx.draw_networkx_edge_labels(G2,pos2,edge_labels=edge_labels, ax=ax2)\n",
        "\n",
        "ax1.set_xlim([1.2*x for x in ax1.get_xlim()])\n",
        "ax2.set_xlim([1.2*x for x in ax2.get_xlim()])\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "id": "eUhWZ9_3jAmi"
      },
      "outputs": [],
      "source": [
        "import pennylane as qml\n",
        "\n",
        "def perm_equivariant_embedding(A, betas, gammas):\n",
        "    \"\"\"\n",
        "    Ansatz to embedd a graph with node and edge weights into a quantum state.\n",
        "\n",
        "    The adjacency matrix A contains the edge weights on the off-diagonal,\n",
        "    as well as the node attributes on the diagonal.\n",
        "\n",
        "    The embedding contains trainable weights 'betas' and 'gammas'.\n",
        "    \"\"\"\n",
        "    n_nodes = len(A)\n",
        "    n_layers = len(betas) # infer the number of layers from the parameters\n",
        "\n",
        "    # initialise in the plus state\n",
        "    for i in range(n_nodes):\n",
        "        qml.Hadamard(i)\n",
        "\n",
        "    for l in range(n_layers):\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            for j in range(i):\n",
        "            \t# factor of 2 due to definition of gate\n",
        "                qml.IsingZZ(2*gammas[l]*A[i,j], wires=[i,j])\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            qml.RX(A[i,i]*betas[l], wires=i)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "glOVsqRvjAmi"
      },
      "source": [
        "We can use this ansatz in a circuit.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 80,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "f143d055-43cf-4347-9343-150ccc1e451e"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 25\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"lightning.kokkos\", wires=n_qubits)\n",
        "\n",
        "@qml.qnode(dev)\n",
        "def eqc(adjacency_matrix, observable, trainable_betas, trainable_gammas):\n",
        "    \"\"\"Circuit that uses the permutation equivariant embedding\"\"\"\n",
        "\n",
        "    perm_equivariant_embedding(adjacency_matrix, trainable_betas, trainable_gammas)\n",
        "    return qml.expval(observable)\n",
        "\n",
        "\n",
        "A = create_data_point(n_qubits)\n",
        "betas = np.random.rand(n_layers)\n",
        "gammas = np.random.rand(n_layers)\n",
        "observable = qml.PauliX(0) @ qml.PauliX(1) @ qml.PauliX(3)\n",
        "\n",
        "qml.draw_mpl(eqc, decimals=2)(A, observable, betas, gammas)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TIHRQVnDjAmi"
      },
      "source": [
        "Validating the equivariance\n",
        "===========================\n",
        "\n",
        "Let\\'s now check if the circuit is really equivariant!\n",
        "\n",
        "This is the expectation value we get using the original adjacency matrix\n",
        "as an input:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "8d1d4995-540e-4e7c-d70a-30c9d6161c72"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.00013554539153222227\n"
          ]
        }
      ],
      "source": [
        "result_A = eqc(A, observable, betas, gammas)\n",
        "print(\"Model output for A:\", result_A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ncmkAwH-jAmj"
      },
      "source": [
        "If we permute the adjacency matrix, this is what we get:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "8b7bcae5-56f2-4b59-a0af-2ef2dbc511af"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.5513774167369957\n"
          ]
        }
      ],
      "source": [
        "perm = [2, 3, 0, 1, 4]\n",
        "A_perm = permute(A, perm)\n",
        "result_Aperm = eqc(A_perm, observable, betas, gammas)\n",
        "print(\"Model output for permutation of A: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZOIqQmysjAmj"
      },
      "source": [
        "Why are the two values different? Well, we constructed an *equivariant*\n",
        "ansatz, not an *invariant* one! Remember, an *invariant* ansatz means\n",
        "that embedding a permutation of the adjacency matrix leads to the same\n",
        "state as an embedding of the original matrix. An *equivariant* ansatz\n",
        "embeds the permuted adjacency matrix into a state where the qubits are\n",
        "permuted as well.\n",
        "\n",
        "As a result, the final state before measurement is only the same if we\n",
        "permute the qubits in the same manner that we permute the input\n",
        "adjacency matrix. We could insert a permutation operator\n",
        "`qml.Permute(perm)` to achieve this, or we simply permute the wires of\n",
        "the observables!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "metadata": {
        "id": "MgYVIMP6jAmj"
      },
      "outputs": [],
      "source": [
        "observable_perm = qml.PauliX(perm[0]) @ qml.PauliX(perm[1]) @ qml.PauliX(perm[3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pb21hBrLjAmj"
      },
      "source": [
        "Now everything should work out!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "1e38fe70-10cf-40d2-cff5-824ca9018b8e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4213426362279188\n"
          ]
        }
      ],
      "source": [
        "result_Aperm = eqc(A_perm, observable_perm, betas, gammas)\n",
        "print(\"Model output for permutation of A, and with permuted observable: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0wblJk9mjAmj"
      },
      "source": [
        "Et voilà!\n",
        "\n",
        "Conclusion\n",
        "==========\n",
        "\n",
        "Equivariant graph embeddings can be combined with other equivariant\n",
        "parts of a quantum machine learning pipeline (like measurements and the\n",
        "cost function). [Skolik et al.\n",
        "(2022)](https://arxiv.org/pdf/2205.06109.pdf), for example, use such a\n",
        "pipeline as part of a reinforcement learning scheme that finds heuristic\n",
        "solutions for the traveling salesman problem. Their simulations compare\n",
        "a fully equivariant model to circuits that break permutation\n",
        "equivariance and show that it performs better, confirming that if we\n",
        "know about structure in our data, we should try to use this knowledge in\n",
        "machine learning.\n",
        "\n",
        "References\n",
        "==========\n",
        "\n",
        "1.  Andrea Skolik, Michele Cattelan, Sheir Yarkoni,Thomas Baeck and\n",
        "    Vedran Dunjko (2022). Equivariant quantum circuits for learning on\n",
        "    weighted graphs.\n",
        "    [arXiv:2205.06109](https://arxiv.org/abs/2205.06109)\n",
        "2.  Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone,\n",
        "    Patrick J. Coles, Frédéric Sauvage, Martín Larocca and Marco Cerezo\n",
        "    (2022). Theory for Equivariant Quantum Neural Networks.\n",
        "    [arXiv:2210.08566](https://arxiv.org/abs/2210.08566)\n",
        "\n",
        "About the author\n",
        "================\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "seconds = time.time()\n",
        "print(\"Time in seconds since end of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "HFTIJBPqph2f",
        "outputId": "30d3ab69-c85c-4c91-9e37-516bf44bbb8a"
      },
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701141239.1057138\n",
            "Tue Nov 28 03:13:59 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "A100",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}